Is it possible to make a neural network to solve this "reaction time test"?
Basically, what you want to do is an anomaly detection at the fastest speed possible. You need to sample the image at two timesteps and if there is a difference you click. The smaller the difference between your timesteps the better it is.
But, you would not need a neural network for it. Since, it is a single colour that will change. A color is represented by a 3-tuple (RGB) so you just need to compare them and if they are different then you click. A single if condition will suffice for it.